Properties

Label 63.4.c.a.62.3
Level $63$
Weight $4$
Character 63.62
Analytic conductor $3.717$
Analytic rank $0$
Dimension $4$
CM discriminant -7
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 8 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 62.3
Root \(-2.57794i\) of defining polynomial
Character \(\chi\) \(=\) 63.62
Dual form 63.4.c.a.62.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.66471i q^{2} +5.22876 q^{4} +18.5203 q^{7} +22.0220i q^{8} +O(q^{10})\) \(q+1.66471i q^{2} +5.22876 q^{4} +18.5203 q^{7} +22.0220i q^{8} +29.3750i q^{11} +30.8308i q^{14} +5.16995 q^{16} -48.9007 q^{22} -181.692i q^{23} -125.000 q^{25} +96.8379 q^{28} -304.463i q^{29} +184.782i q^{32} -10.5830 q^{37} -534.442 q^{43} +153.595i q^{44} +302.464 q^{46} +343.000 q^{49} -208.088i q^{50} +768.909i q^{53} +407.853i q^{56} +506.840 q^{58} -266.248 q^{64} +740.000 q^{67} -1178.70i q^{71} -17.6176i q^{74} +544.032i q^{77} -1384.00 q^{79} -889.688i q^{86} -646.895 q^{88} -950.024i q^{92} +570.994i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 32q^{4} + O(q^{10}) \) \( 4q - 32q^{4} + 444q^{16} - 820q^{22} - 500q^{25} + 980q^{28} - 748q^{46} + 1372q^{49} + 260q^{58} - 3552q^{64} + 2960q^{67} - 5536q^{79} + 8260q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66471i 0.588562i 0.955719 + 0.294281i \(0.0950802\pi\)
−0.955719 + 0.294281i \(0.904920\pi\)
\(3\) 0 0
\(4\) 5.22876 0.653595
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 18.5203 1.00000
\(8\) 22.0220i 0.973243i
\(9\) 0 0
\(10\) 0 0
\(11\) 29.3750i 0.805172i 0.915382 + 0.402586i \(0.131889\pi\)
−0.915382 + 0.402586i \(0.868111\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 30.8308i 0.588562i
\(15\) 0 0
\(16\) 5.16995 0.0807804
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −48.9007 −0.473894
\(23\) − 181.692i − 1.64719i −0.567176 0.823597i \(-0.691964\pi\)
0.567176 0.823597i \(-0.308036\pi\)
\(24\) 0 0
\(25\) −125.000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 96.8379 0.653595
\(29\) − 304.463i − 1.94956i −0.223165 0.974781i \(-0.571639\pi\)
0.223165 0.974781i \(-0.428361\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 184.782i 1.02079i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.5830 −0.0470226 −0.0235113 0.999724i \(-0.507485\pi\)
−0.0235113 + 0.999724i \(0.507485\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −534.442 −1.89539 −0.947693 0.319183i \(-0.896592\pi\)
−0.947693 + 0.319183i \(0.896592\pi\)
\(44\) 153.595i 0.526256i
\(45\) 0 0
\(46\) 302.464 0.969476
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 343.000 1.00000
\(50\) − 208.088i − 0.588562i
\(51\) 0 0
\(52\) 0 0
\(53\) 768.909i 1.99279i 0.0848489 + 0.996394i \(0.472959\pi\)
−0.0848489 + 0.996394i \(0.527041\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 407.853i 0.973243i
\(57\) 0 0
\(58\) 506.840 1.14744
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −266.248 −0.520016
\(65\) 0 0
\(66\) 0 0
\(67\) 740.000 1.34933 0.674667 0.738122i \(-0.264287\pi\)
0.674667 + 0.738122i \(0.264287\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 1178.70i − 1.97022i −0.171931 0.985109i \(-0.555000\pi\)
0.171931 0.985109i \(-0.445000\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) − 17.6176i − 0.0276757i
\(75\) 0 0
\(76\) 0 0
\(77\) 544.032i 0.805172i
\(78\) 0 0
\(79\) −1384.00 −1.97104 −0.985520 0.169559i \(-0.945766\pi\)
−0.985520 + 0.169559i \(0.945766\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) − 889.688i − 1.11555i
\(87\) 0 0
\(88\) −646.895 −0.783628
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) − 950.024i − 1.07660i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 570.994i 0.588562i
\(99\) 0 0
\(100\) −653.595 −0.653595
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1280.01 −1.17288
\(107\) 20.9231i 0.0189039i 0.999955 + 0.00945193i \(0.00300869\pi\)
−0.999955 + 0.00945193i \(0.996991\pi\)
\(108\) 0 0
\(109\) 2275.35 1.99944 0.999718 0.0237260i \(-0.00755292\pi\)
0.999718 + 0.0237260i \(0.00755292\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 95.7488 0.0807804
\(113\) 1157.60i 0.963699i 0.876254 + 0.481849i \(0.160035\pi\)
−0.876254 + 0.481849i \(0.839965\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) − 1591.96i − 1.27422i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 468.111 0.351699
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2000.00 1.39741 0.698706 0.715409i \(-0.253760\pi\)
0.698706 + 0.715409i \(0.253760\pi\)
\(128\) 1035.03i 0.714725i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1231.88i 0.794167i
\(135\) 0 0
\(136\) 0 0
\(137\) 2752.87i 1.71674i 0.513031 + 0.858370i \(0.328522\pi\)
−0.513031 + 0.858370i \(0.671478\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1962.18 1.15960
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −55.3360 −0.0307337
\(149\) 1931.33i 1.06188i 0.847409 + 0.530941i \(0.178161\pi\)
−0.847409 + 0.530941i \(0.821839\pi\)
\(150\) 0 0
\(151\) −2248.89 −1.21200 −0.606000 0.795465i \(-0.707227\pi\)
−0.606000 + 0.795465i \(0.707227\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −905.653 −0.473894
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) − 2303.95i − 1.16008i
\(159\) 0 0
\(160\) 0 0
\(161\) − 3364.99i − 1.64719i
\(162\) 0 0
\(163\) −1780.00 −0.855340 −0.427670 0.903935i \(-0.640665\pi\)
−0.427670 + 0.903935i \(0.640665\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 2197.00 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −2794.47 −1.23881
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −2315.03 −1.00000
\(176\) 151.867i 0.0650421i
\(177\) 0 0
\(178\) 0 0
\(179\) − 1575.84i − 0.658010i −0.944328 0.329005i \(-0.893287\pi\)
0.944328 0.329005i \(-0.106713\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4001.22 1.60312
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 5255.29i − 1.99089i −0.0953502 0.995444i \(-0.530397\pi\)
0.0953502 0.995444i \(-0.469603\pi\)
\(192\) 0 0
\(193\) −2772.75 −1.03413 −0.517064 0.855947i \(-0.672975\pi\)
−0.517064 + 0.855947i \(0.672975\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1793.46 0.653595
\(197\) 5147.21i 1.86154i 0.365603 + 0.930771i \(0.380863\pi\)
−0.365603 + 0.930771i \(0.619137\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) − 2752.75i − 0.973243i
\(201\) 0 0
\(202\) 0 0
\(203\) − 5638.73i − 1.94956i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1772.65 −0.578363 −0.289181 0.957274i \(-0.593383\pi\)
−0.289181 + 0.957274i \(0.593383\pi\)
\(212\) 4020.44i 1.30248i
\(213\) 0 0
\(214\) −34.8308 −0.0111261
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 3787.78i 1.17679i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 3422.22i 1.02079i
\(225\) 0 0
\(226\) −1927.06 −0.567197
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6704.87 1.89740
\(233\) − 412.009i − 0.115844i −0.998321 0.0579219i \(-0.981553\pi\)
0.998321 0.0579219i \(-0.0184474\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5533.66i 1.49767i 0.662757 + 0.748834i \(0.269386\pi\)
−0.662757 + 0.748834i \(0.730614\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 779.267i 0.206997i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 5337.20 1.32627
\(254\) 3329.41i 0.822464i
\(255\) 0 0
\(256\) −3853.01 −0.940677
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) −196.000 −0.0470226
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2470.04i 0.579123i 0.957159 + 0.289561i \(0.0935094\pi\)
−0.957159 + 0.289561i \(0.906491\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 3869.28 0.881917
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −4582.71 −1.01041
\(275\) − 3671.87i − 0.805172i
\(276\) 0 0
\(277\) 7310.00 1.58561 0.792807 0.609472i \(-0.208619\pi\)
0.792807 + 0.609472i \(0.208619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 8982.08i − 1.90685i −0.301625 0.953427i \(-0.597529\pi\)
0.301625 0.953427i \(-0.402471\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) − 6163.11i − 1.28772i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4913.00 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) − 233.059i − 0.0457644i
\(297\) 0 0
\(298\) −3215.09 −0.624983
\(299\) 0 0
\(300\) 0 0
\(301\) −9898.00 −1.89539
\(302\) − 3743.74i − 0.713337i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 2844.61i 0.526256i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −7236.60 −1.28826
\(317\) 1349.97i 0.239185i 0.992823 + 0.119593i \(0.0381588\pi\)
−0.992823 + 0.119593i \(0.961841\pi\)
\(318\) 0 0
\(319\) 8943.58 1.56973
\(320\) 0 0
\(321\) 0 0
\(322\) 5601.71 0.969476
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) − 2963.18i − 0.503421i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −5106.30 −0.847938 −0.423969 0.905677i \(-0.639364\pi\)
−0.423969 + 0.905677i \(0.639364\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11916.5 −1.92621 −0.963103 0.269135i \(-0.913262\pi\)
−0.963103 + 0.269135i \(0.913262\pi\)
\(338\) 3657.36i 0.588562i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 6352.45 1.00000
\(344\) − 11769.5i − 1.84467i
\(345\) 0 0
\(346\) 0 0
\(347\) 11568.6i 1.78972i 0.446347 + 0.894860i \(0.352725\pi\)
−0.446347 + 0.894860i \(0.647275\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) − 3853.85i − 0.588562i
\(351\) 0 0
\(352\) −5427.97 −0.821909
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 2623.31 0.387280
\(359\) 1996.13i 0.293459i 0.989177 + 0.146729i \(0.0468746\pi\)
−0.989177 + 0.146729i \(0.953125\pi\)
\(360\) 0 0
\(361\) 6859.00 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) − 939.339i − 0.133061i
\(369\) 0 0
\(370\) 0 0
\(371\) 14240.4i 1.99279i
\(372\) 0 0
\(373\) 13970.0 1.93925 0.969624 0.244602i \(-0.0786573\pi\)
0.969624 + 0.244602i \(0.0786573\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 8704.52 1.17974 0.589870 0.807498i \(-0.299179\pi\)
0.589870 + 0.807498i \(0.299179\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8748.51 1.17176
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) − 4615.81i − 0.608649i
\(387\) 0 0
\(388\) 0 0
\(389\) 15337.9i 1.99913i 0.0294496 + 0.999566i \(0.490625\pi\)
−0.0294496 + 0.999566i \(0.509375\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 7553.54i 0.973243i
\(393\) 0 0
\(394\) −8568.59 −1.09563
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −646.243 −0.0807804
\(401\) − 10169.8i − 1.26648i −0.773956 0.633239i \(-0.781725\pi\)
0.773956 0.633239i \(-0.218275\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 9386.82 1.14744
\(407\) − 310.876i − 0.0378612i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −15262.0 −1.76680 −0.883402 0.468616i \(-0.844753\pi\)
−0.883402 + 0.468616i \(0.844753\pi\)
\(422\) − 2950.95i − 0.340402i
\(423\) 0 0
\(424\) −16932.9 −1.93947
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 109.402i 0.0123555i
\(429\) 0 0
\(430\) 0 0
\(431\) 5007.24i 0.559606i 0.960057 + 0.279803i \(0.0902692\pi\)
−0.960057 + 0.279803i \(0.909731\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11897.2 1.30682
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 12011.8i − 1.28826i −0.764917 0.644129i \(-0.777220\pi\)
0.764917 0.644129i \(-0.222780\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −4930.99 −0.520016
\(449\) − 15219.6i − 1.59968i −0.600213 0.799841i \(-0.704917\pi\)
0.600213 0.799841i \(-0.295083\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6052.81i 0.629868i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17821.8 −1.82422 −0.912109 0.409947i \(-0.865547\pi\)
−0.912109 + 0.409947i \(0.865547\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −8440.00 −0.847171 −0.423585 0.905856i \(-0.639229\pi\)
−0.423585 + 0.905856i \(0.639229\pi\)
\(464\) − 1574.06i − 0.157486i
\(465\) 0 0
\(466\) 685.873 0.0681813
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 13705.0 1.34933
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 15699.2i − 1.52611i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −9211.91 −0.881471
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2447.64 0.229868
\(485\) 0 0
\(486\) 0 0
\(487\) −3296.61 −0.306742 −0.153371 0.988169i \(-0.549013\pi\)
−0.153371 + 0.988169i \(0.549013\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8998.48i 0.827079i 0.910486 + 0.413540i \(0.135708\pi\)
−0.910486 + 0.413540i \(0.864292\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 21829.8i − 1.97022i
\(498\) 0 0
\(499\) 21086.6 1.89172 0.945859 0.324577i \(-0.105222\pi\)
0.945859 + 0.324577i \(0.105222\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8884.87i 0.780594i
\(507\) 0 0
\(508\) 10457.5 0.913341
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1866.13i 0.161079i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) − 326.282i − 0.0276757i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −4111.89 −0.340850
\(527\) 0 0
\(528\) 0 0
\(529\) −20845.1 −1.71325
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 16296.3i 1.31323i
\(537\) 0 0
\(538\) 0 0
\(539\) 10075.6i 0.805172i
\(540\) 0 0
\(541\) 15878.0 1.26183 0.630914 0.775853i \(-0.282680\pi\)
0.630914 + 0.775853i \(0.282680\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12980.0 1.01460 0.507299 0.861770i \(-0.330644\pi\)
0.507299 + 0.861770i \(0.330644\pi\)
\(548\) 14394.1i 1.12205i
\(549\) 0 0
\(550\) 6112.58 0.473894
\(551\) 0 0
\(552\) 0 0
\(553\) −25632.0 −1.97104
\(554\) 12169.0i 0.933233i
\(555\) 0 0
\(556\) 0 0
\(557\) − 2807.99i − 0.213606i −0.994280 0.106803i \(-0.965939\pi\)
0.994280 0.106803i \(-0.0340613\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 14952.5 1.12230
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 25957.2 1.91750
\(569\) 16481.1i 1.21428i 0.794596 + 0.607138i \(0.207683\pi\)
−0.794596 + 0.607138i \(0.792317\pi\)
\(570\) 0 0
\(571\) 6788.00 0.497494 0.248747 0.968569i \(-0.419981\pi\)
0.248747 + 0.968569i \(0.419981\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22711.5i 1.64719i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) − 8178.70i − 0.588562i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −22586.7 −1.60454
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −54.7136 −0.00379850
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10098.4i 0.694040i
\(597\) 0 0
\(598\) 0 0
\(599\) − 28622.4i − 1.95239i −0.216899 0.976194i \(-0.569594\pi\)
0.216899 0.976194i \(-0.430406\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) − 16477.3i − 1.11555i
\(603\) 0 0
\(604\) −11758.9 −0.792156
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −15010.0 −0.988986 −0.494493 0.869182i \(-0.664646\pi\)
−0.494493 + 0.869182i \(0.664646\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −11980.7 −0.783628
\(617\) − 19836.0i − 1.29428i −0.762372 0.647139i \(-0.775965\pi\)
0.762372 0.647139i \(-0.224035\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15625.0 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 26192.0 1.65244 0.826218 0.563351i \(-0.190488\pi\)
0.826218 + 0.563351i \(0.190488\pi\)
\(632\) − 30478.4i − 1.91830i
\(633\) 0 0
\(634\) −2247.30 −0.140775
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 14888.4i 0.923885i
\(639\) 0 0
\(640\) 0 0
\(641\) − 28353.5i − 1.74711i −0.486729 0.873553i \(-0.661810\pi\)
0.486729 0.873553i \(-0.338190\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) − 17594.7i − 1.07660i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −9307.19 −0.559045
\(653\) 32948.9i 1.97456i 0.158976 + 0.987282i \(0.449181\pi\)
−0.158976 + 0.987282i \(0.550819\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22614.9i 1.33680i 0.743803 + 0.668399i \(0.233020\pi\)
−0.743803 + 0.668399i \(0.766980\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) − 8500.48i − 0.499065i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −55318.5 −3.21130
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 9609.37 0.550392 0.275196 0.961388i \(-0.411257\pi\)
0.275196 + 0.961388i \(0.411257\pi\)
\(674\) − 19837.4i − 1.13369i
\(675\) 0 0
\(676\) 11487.6 0.653595
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 31645.9i − 1.77291i −0.462813 0.886456i \(-0.653160\pi\)
0.462813 0.886456i \(-0.346840\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 10575.0i 0.588562i
\(687\) 0 0
\(688\) −2763.04 −0.153110
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −19258.2 −1.05336
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −12104.7 −0.653595
\(701\) 23110.9i 1.24520i 0.782539 + 0.622602i \(0.213924\pi\)
−0.782539 + 0.622602i \(0.786076\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) − 7821.04i − 0.418703i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 35611.8 1.88636 0.943180 0.332281i \(-0.107818\pi\)
0.943180 + 0.332281i \(0.107818\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) − 8239.68i − 0.430072i
\(717\) 0 0
\(718\) −3322.97 −0.172719
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11418.2i 0.588562i
\(723\) 0 0
\(724\) 0 0
\(725\) 38057.8i 1.94956i
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 33573.5 1.68143
\(737\) 21737.5i 1.08645i
\(738\) 0 0
\(739\) −25324.0 −1.26057 −0.630283 0.776365i \(-0.717061\pi\)
−0.630283 + 0.776365i \(0.717061\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −23706.1 −1.17288
\(743\) − 4655.40i − 0.229865i −0.993373 0.114933i \(-0.963335\pi\)
0.993373 0.114933i \(-0.0366652\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 23255.9i 1.14137i
\(747\) 0 0
\(748\) 0 0
\(749\) 387.501i 0.0189039i
\(750\) 0 0
\(751\) 41088.5 1.99646 0.998230 0.0594732i \(-0.0189421\pi\)
0.998230 + 0.0594732i \(0.0189421\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22848.7 1.09703 0.548514 0.836141i \(-0.315194\pi\)
0.548514 + 0.836141i \(0.315194\pi\)
\(758\) 14490.5i 0.694350i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 42140.0 1.99944
\(764\) − 27478.6i − 1.30123i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14498.0 −0.675901
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −25533.1 −1.17661
\(779\) 0 0
\(780\) 0 0
\(781\) 34624.2 1.58636
\(782\) 0 0
\(783\) 0 0
\(784\) 1773.29 0.0807804
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 26913.5i 1.21669i
\(789\) 0 0
\(790\) 0 0
\(791\) 21439.1i 0.963699i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) − 23097.8i − 1.02079i
\(801\) 0 0
\(802\) 16929.8 0.745402
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 7405.65i − 0.321840i −0.986967 0.160920i \(-0.948554\pi\)
0.986967 0.160920i \(-0.0514461\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) − 29483.5i − 1.27422i
\(813\) 0 0
\(814\) 517.516 0.0222837
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 43395.4i 1.84471i 0.386339 + 0.922357i \(0.373739\pi\)
−0.386339 + 0.922357i \(0.626261\pi\)
\(822\) 0 0
\(823\) −46240.0 −1.95848 −0.979238 0.202716i \(-0.935023\pi\)
−0.979238 + 0.202716i \(0.935023\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 46002.9i − 1.93431i −0.254179 0.967157i \(-0.581805\pi\)
0.254179 0.967157i \(-0.418195\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −68308.5 −2.80079
\(842\) − 25406.7i − 1.03987i
\(843\) 0 0
\(844\) −9268.77 −0.378015
\(845\) 0 0
\(846\) 0 0
\(847\) 8669.54 0.351699
\(848\) 3975.22i 0.160978i
\(849\) 0 0
\(850\) 0 0
\(851\) 1922.85i 0.0774553i
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −460.768 −0.0183980
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −8335.58 −0.329363
\(863\) − 47169.0i − 1.86055i −0.366868 0.930273i \(-0.619570\pi\)
0.366868 0.930273i \(-0.380430\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 40655.0i − 1.58703i
\(870\) 0 0
\(871\) 0 0
\(872\) 50107.6i 1.94594i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6550.00 −0.252198 −0.126099 0.992018i \(-0.540246\pi\)
−0.126099 + 0.992018i \(0.540246\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) −43014.6 −1.63936 −0.819681 0.572820i \(-0.805850\pi\)
−0.819681 + 0.572820i \(0.805850\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 19996.1 0.758220
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 37040.5 1.39741
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 19169.1i 0.714725i
\(897\) 0 0
\(898\) 25336.1 0.941512
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −25492.7 −0.937913
\(905\) 0 0
\(906\) 0 0
\(907\) −14250.0 −0.521680 −0.260840 0.965382i \(-0.584000\pi\)
−0.260840 + 0.965382i \(0.584000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1065.41i 0.0387473i 0.999812 + 0.0193736i \(0.00616720\pi\)
−0.999812 + 0.0193736i \(0.993833\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) − 29668.0i − 1.07367i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −51301.1 −1.84142 −0.920711 0.390244i \(-0.872391\pi\)
−0.920711 + 0.390244i \(0.872391\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1322.88 0.0470226
\(926\) − 14050.1i − 0.498613i
\(927\) 0 0
\(928\) 56259.3 1.99009
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) − 2154.29i − 0.0757149i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 22814.8i 0.794167i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 26134.6 0.898211
\(947\) − 57034.5i − 1.95710i −0.206013 0.978549i \(-0.566049\pi\)
0.206013 0.978549i \(-0.433951\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 56795.7i − 1.93053i −0.261276 0.965264i \(-0.584143\pi\)
0.261276 0.965264i \(-0.415857\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 28934.2i 0.978868i
\(957\) 0 0
\(958\) 0 0
\(959\) 50983.8i 1.71674i
\(960\) 0 0
\(961\) 29791.0 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 52040.0 1.73060 0.865302 0.501251i \(-0.167127\pi\)
0.865302 + 0.501251i \(0.167127\pi\)
\(968\) 10308.7i 0.342288i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) − 5487.88i − 0.180537i
\(975\) 0 0
\(976\) 0 0
\(977\) 60603.4i 1.98452i 0.124182 + 0.992259i \(0.460369\pi\)
−0.124182 + 0.992259i \(0.539631\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −14979.8 −0.486788
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 97103.9i 3.12207i
\(990\) 0 0
\(991\) −24155.7 −0.774300 −0.387150 0.922017i \(-0.626540\pi\)
−0.387150 + 0.922017i \(0.626540\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 36340.1 1.15960
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 35103.0i 1.11339i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.4.c.a.62.3 yes 4
3.2 odd 2 inner 63.4.c.a.62.2 4
4.3 odd 2 1008.4.k.a.881.1 4
7.2 even 3 441.4.p.b.80.3 8
7.3 odd 6 441.4.p.b.215.2 8
7.4 even 3 441.4.p.b.215.2 8
7.5 odd 6 441.4.p.b.80.3 8
7.6 odd 2 CM 63.4.c.a.62.3 yes 4
12.11 even 2 1008.4.k.a.881.2 4
21.2 odd 6 441.4.p.b.80.2 8
21.5 even 6 441.4.p.b.80.2 8
21.11 odd 6 441.4.p.b.215.3 8
21.17 even 6 441.4.p.b.215.3 8
21.20 even 2 inner 63.4.c.a.62.2 4
28.27 even 2 1008.4.k.a.881.1 4
84.83 odd 2 1008.4.k.a.881.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.c.a.62.2 4 3.2 odd 2 inner
63.4.c.a.62.2 4 21.20 even 2 inner
63.4.c.a.62.3 yes 4 1.1 even 1 trivial
63.4.c.a.62.3 yes 4 7.6 odd 2 CM
441.4.p.b.80.2 8 21.2 odd 6
441.4.p.b.80.2 8 21.5 even 6
441.4.p.b.80.3 8 7.2 even 3
441.4.p.b.80.3 8 7.5 odd 6
441.4.p.b.215.2 8 7.3 odd 6
441.4.p.b.215.2 8 7.4 even 3
441.4.p.b.215.3 8 21.11 odd 6
441.4.p.b.215.3 8 21.17 even 6
1008.4.k.a.881.1 4 4.3 odd 2
1008.4.k.a.881.1 4 28.27 even 2
1008.4.k.a.881.2 4 12.11 even 2
1008.4.k.a.881.2 4 84.83 odd 2